As you surmised, it is just an sound change: the long vowel shortened.
This is made clear by recorded early citations. Earlier citations for okiagari kobōshi--with the long vowel--may be found from mid-Muromachi texts. (For example "Jippon Ōgi" 十本扇.) Early citations for okiagari koboshi--with the short vowel--may be found from early Edo period. (For example "Kyōgonki" 狂言記.)
The word kobōshi also exists. Early citations from the 10th century. Note that there does not seem to be a corresponding *koboshi, though. That may give a hint as to why okiagari koboshi came about: to distinguish this self-righting dharma doll from "a young monk" (kobōshi). But that is only a guess.
In modern Japanese, the version with the short vowel is most common. That is why you will likely find in regular dictionaries.
For the record, you may also find the following expressions as well: okikaeri kobōshi and okiyagari / okyagari koboshi, all with the same meaning.